Okay, so I think that one of the most major concepts that we covered this year was knowing the Trig Identites:
csc = 1/sin x
sec = 1/cos x
cot x = 1/tan x
sin (-x) = -sin x
cos (-x) = cos x
csc (-x) = -csc x
sec (-x) = sec x
tan (-x) = -tan x
cot (-x) = -cot x
sin^2 x+cos^2 x = 1
1+tan^2 x = sec^2 x
1+cot^2 x = csc^2 x
sin x = cos(90*-x)
tan x = cot (90*-x)
sec x = csc (90*-x)
cos x = sin (90*-x)
cot x = tan (90*-x)
csc x = sec (90*-x)
tan x = sinx/cosx
cot x = cosx/sinx
To me this and the trig chart were two of the most important things we learned because you had to memorize all these identities, and without them you would not be able to do a lot of the problems in trig, and memorizing the chart helps you simplify an answer to the simplest form possible.
An activity that really helped me this year was when B-rob told me that the whole trig chart can be derived by just knowing the first few lines. sin cos and tan's answers can be flipped and that gives you the csc sec and cot's answers.
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